Problem: Solve for $x$ and $y$ using elimination. ${x-5y = -15}$ ${-x+3y = 5}$
Answer: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $x$ and $-x$ cancel out. $-2y = -10$ $\dfrac{-2y}{{-2}} = \dfrac{-10}{{-2}}$ ${y = 5}$ Now that you know ${y = 5}$ , plug it back into $\thinspace {x-5y = -15}\thinspace$ to find $x$ ${x - 5}{(5)}{= -15}$ $x-25 = -15$ $x-25{+25} = -15{+25}$ ${x = 10}$ You can also plug ${y = 5}$ into $\thinspace {-x+3y = 5}\thinspace$ and get the same answer for $x$ : ${-x + 3}{(5)}{= 5}$ ${x = 10}$